“Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020

“Unfunded Liabilities” and UncertainFiscal Financing

Troy Davig*, Eric M. Leeper† & Todd B. Walker†

*Federal Reserve Bank of Kansas City† Indiana University

February 2010Banco de Espana Conference

Introduction

I Profound uncertainty surrounds the funding of futurepromised transfers in the U.S.

“Unfunded Liabilities”

Social Security

1962 1972 1982 1992 2002 2012 2022 2032 2042 2052 2062 2072 20820

5

10

15

20

25

30

35

Percentage

ofGDP

Source: CBO Long-Term Budget Outlook (June 2009)


Social Security

Medicare and Medicaid

1962 1972 1982 1992 2002 2012 2022 2032 2042 2052 2062 2072 20820

5

10

15

20

25

30

35

Percentage

ofGDP



Social Security


Other Federal Non-interest Spending

1962 1972 1982 1992 2002 2012 2022 2032 2042 2052 2062 2072 20820

5

10

15

20

25

30

35

Percentage

ofGDP


Introduction


I Unfunded liabilities is not an economically meaningfulterm—inconsistent with equilibrium

I The government will renege on promised transfers(i.e. “liabilities” do not exist)

I The government will fund the promised transfers(i.e. liabilities are not “unfunded”)

I CBO projects debt rising to over 700% of GDP

Introduction






Rolling Spending Commitments into Debt

1790

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1810

1820

1830

1840

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1880

1890

1900

1910

1920

1930

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1990

2000

2010

2020

2030

2040

2050

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0

100

200

300

400

500

600

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800

Percentage

ofGDP

Alternative Fiscal Scenario

Extended-Baseline Scenario

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1


Introduction






⇒ future policy will change

...how and when?

Introduction






⇒ future policy will change...how and when?

Introduction

I Nearly every advanced economyfaces this problem

What We Do

I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem

1. Reneging on transfers⇒ “Third Rail of Politics”

2. Distortionary taxation⇒ Fiscal limit

3. Sacrificing inflation target⇒ Volatile inflation

4. Inflation financing (printing presses)⇒ Fiscal limithere also

5. Debt default⇒ Are U.S. Treasuries risk-free assets?

What We Do


1. Reneging on transfers

⇒ “Third Rail of Politics”





What We Do







What We Do



2. Distortionary taxation

⇒ Fiscal limit




What We Do







What We Do




3. Sacrificing inflation target

⇒ Volatile inflation



What We Do







What We Do





4. Inflation financing (printing presses)

⇒ Fiscal limithere also


What We Do







What We Do






5. Debt default

⇒ Are U.S. Treasuries risk-free assets?

What We Do







What We Do





We model a combination of 1–3, emphasizinguncertainty about which policies adjust and whenpolicies adjust.

What We Do


I Allow for switching among policy solutions

I Model fiscal limit as random variable = f (fiscalvariables)

I Focus on expectational effects in otherwise standardmacroeconomic DSGE model

What We Do





What We Do





Analytic Intuition: Simple ModelI Consider a flexible price, cashless, endowment

economy

I The consumption Euler equation reduces to theFisher equation

1Rt

= βEt

(Pt

Pt+1

)I Transfers grow at rate µ financed by lump-sum taxes

and debt

zt = (1− µ)z∗ + µzt−1 + εt, µ < 1/β

I Government’s Budget Constraint:Bt

Pt+ τt = zt +

Rt−1Bt−1

Pt


economy


1Rt

= βEt

(Pt

Pt+1

)

I Transfers grow at rate µ financed by lump-sum taxesand debt

zt = (1− µ)z∗ + µzt−1 + εt, µ < 1/β


Pt+ τt = zt +

Rt−1Bt−1

Pt


economy


1Rt

= βEt

(Pt

Pt+1


and debt

zt = (1− µ)z∗ + µzt−1 + εt, µ < 1/β


Pt+ τt = zt +

Rt−1Bt−1

Pt


economy


1Rt

= βEt

(Pt

Pt+1


and debt

zt = (1− µ)z∗ + µzt−1 + εt, µ < 1/β


Pt+ τt = zt +

Rt−1Bt−1

Pt

Analytic Intuition: Policy Specification

At time T economy reaches fiscal limit

Regime 1t = 0, 1, . . . ,T − 1

Monetary Policy R−1t = R∗−1 + α

(Pt−1

Pt− 1

π∗

)Tax Policy τt = τ ∗ + γ

(Bt−1Pt−1− b∗

)



Regime 1t = 0, 1, . . . ,T − 1


(Pt−1

Pt− 1

π∗

)Tax Policy τt = τ ∗ + γ

(Bt−1Pt−1− b∗

)



Regime 1 Regime 2t = 0, 1, . . . ,T − 1 t = T,T + 1, . . .


(Pt−1

Pt− 1

π∗

)R−1

t = R∗−1

Tax Policy τt = τ ∗ + γ(

Bt−1Pt−1− b∗

)τt = τmax



Regime 1 Regime 2t = 0, 1, . . . ,T − 1 t = T,T + 1, . . .


(Pt−1

Pt− 1

π∗

)R−1

t = R∗−1

Tax Policy τt = τ ∗ + γ(


)τt = τmax

Fiscal limit may be economic (peak of Laffer curve) orpolitical (intolerance of taxation)

Analytic Intuition: Polar Case 1

If Regime 1 were absorbing state (No Fiscal Limit)

α

βEt

(Pt

Pt+1− 1π∗

)=

Pt−1

Pt− 1π∗

(Regime 1)

Et−1

(Bt

Pt− b∗

)= Et−1(zt − z∗) + (β−1 − γ)

(Bt−1

Pt−1− b∗

)α/β > 1, β−1 − γ < 1⇒ Equilibrium πt = π∗

A Standard Monetary Equilibrium



α

βEt

(Pt

Pt+1− 1π∗

)=

Pt−1

Pt− 1π∗

(Regime 1)

Et−1

(Bt

Pt− b∗

)= Et−1(zt − z∗) + (β−1 − γ)

(Bt−1

Pt−1− b∗





α

βEt

(Pt

Pt+1− 1π∗

)=

Pt−1

Pt− 1π∗

(Regime 1)

Et−1

(Bt

Pt− b∗

)= Et−1(zt − z∗) + (β−1 − γ)

(Bt−1

Pt−1− b∗

)

α/β > 1, β−1 − γ < 1⇒ Equilibrium πt = π∗




α

βEt

(Pt

Pt+1− 1π∗

)=

Pt−1

Pt− 1π∗

(Regime 1)

Et−1

(Bt

Pt− b∗

)= Et−1(zt − z∗) + (β−1 − γ)

(Bt−1

Pt−1− b∗




If Regime 2 were absorbing state

Et

(Pt

Pt+1

)=

1βR∗

=1π∗

(Regime 2)

Bt

Pt=

(β

1− β

)τ ∗ − Et

∞∑j=1

βjzt+j

α = 0, γ = 0⇒ Actual Inflation

Pt =Rt−1Bt−1(

11−β

)τ ∗ − Et

∑∞j=0 β

jzt+j

A Standard Fiscal Equilibrium



Et

(Pt

Pt+1

)=

1βR∗

=1π∗

(Regime 2)

Bt

Pt=

(β

1− β

)τ ∗ − Et

∞∑j=1

βjzt+j


Pt =Rt−1Bt−1(

11−β

)τ ∗ − Et

∑∞j=0 β

jzt+j




Et

(Pt

Pt+1

)=

1βR∗

=1π∗

(Regime 2)

Bt

Pt=

(β

1− β

)τ ∗ − Et

∞∑j=1

βjzt+j


Pt =Rt−1Bt−1(

11−β

)τ ∗ − Et

∑∞j=0 β

jzt+j




Et

(Pt

Pt+1

)=

1βR∗

=1π∗

(Regime 2)

Bt

Pt=

(β

1− β

)τ ∗ − Et

∞∑j=1

βjzt+j


Pt =Rt−1Bt−1(

11−β

)τ ∗ − Et

∑∞j=0 β

jzt+j


Fiscal Limit: Reneging

t = 0, 1, . . . ,T − 1 t = T,T + 1, . . .


(Pt−1

Pt− 1

π∗

)same

Tax Policy τt = τ∗ + γ(


)τt = τmax

Transfer Policy zt λtzt

Et−1[Bt/Pt] + τmax = Et−1λtzt + (β−1 − γ)(Bt−1/Pt−1)

πt = π∗


Fiscal Limit: No Reneging

t = 0, 1, . . . ,T − 1 t = T,T + 1, . . .


(Pt−1

Pt− 1

π∗

)R−1

t = R∗−1

Tax Policy τt = τ∗ + γ(


)τt = τmax

Transfer Policy zt same

Et

(Pt

Pt+1− 1π∗

)=α

β

(Pt−1

Pt− 1π∗

),

α

β> 1

Pt = f (zt; γ, µ, β, π∗)

A New Fiscal Equilibrium Before the Limit

Analytic Intuition: Debt

0 5 10 15 20 25 30 35 40 45 500.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

0.6

0.62

0.64

Debt inRegime 2

Debt−GDP Target

Fiscal LimitT = 50

Analytic Intuition: Debt

0 5 10 15 20 25 30 35 40 45 500.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

0.6

0.62

0.64

Debt inRegime 2

Debt−GDP Target

Fiscal LimitT = 50

Debt WhenFiscal Limit at T

Analytic Intuition: Inflation

0 5 10 15 20 25 30 35 40 45 50

0.8

0.9

1

1.1

1.2

1.3

InflationTarget

Inflation inRegime 2

Fiscal LimitT = 50

Analytic Intuition: Inflation

0 5 10 15 20 25 30 35 40 45 50

0.8

0.9

1

1.1

1.2

1.3

InflationTarget


Inflation WhenFiscal Limitat T = 50

Fiscal LimitT = 50

Analytic Intuition: Expected Inflation

0 5 10 15 20 25 30 35 40 45 50

0.8

0.9

1

1.1

1.2

1.3

InflationTarget


Expected InflationWhen Fiscal Limit

at T = 50 Inflation WhenFiscal Limitat T = 50

Fiscal LimitT = 50

Fiscal Limit: Implications

I Expectations of post-limit policies determine pre-limitequilibrium

I Inflation and debt not anchored on targets

I Expectations—and equilibrium—time varying asapproach limit

I Pre-limit equilibrium converges to post-limitequilibrium

Promised Transfers in a DSGE Model

Other Federal Non-interest Spending


Social Security

1962 1972 1982 1992 2002 2012 2022 2032 2042 2052 2062 2072 20820

5

10

15

20

25

30

35

Percentage

ofGDP

Revenues Model

Full-Blown Model

I Standard DSGE model: capital accumulation, stickyprices, distorting taxation

I Government announces path of promised transfers

I Government debt and taxes grow until the economyhits fiscal limit

I Specify a set of policies that stabilize debt after fiscallimit

I Multiple layers of policy uncertainty

Households and Firms

I Household utility depends on consumption, leisureand real balances

I Household’s budget constraint is

Ct + Kt +Bt

Pt+

Mt

Pt≤ (1− τt)

(Wt

PtNt + Rk

t Kt−1

)

+(1− δ)Kt−1 +Rt−1Bt−1

Pt+

Mt−1

Pt+ λtzt +

Dt

Pt

I Firms set prices as a markup over marginal costs(Rotemberg costly adjustment)

Initial Period: Stationary Transfers

1

MP: Rt = R∗ + α(πt − π∗), α > 1/β

FP: τt = τ ∗ + γ(bt−1/Yt−1 − b∗), γ > r

Transfers: zt = (1− ρz)z∗ + ρzzt−1 + εt

Non-Stationary Promised Transfers

1

MP: Rt = R∗ + α(πt − π∗), α > 1/β

FP: τt = τ ∗ + γ(bt−1/Yt−1 − b∗), γ > r

Transfers: zt = µzt−1 + εt, µ > 1

PZ

Fiscal Limit

1

FP: τt = τmax

PL,t

PL,t =exp(η0+η1(τt−1−τ∗))

1+exp(η0+η1(τt−1−τ∗))

Fiscal Limit: Regime 1 AM/AF/PT

1

MP: Rt = R∗ + α(πt − π∗), α > 1/β

FP: τt = τmax

Transfers: λtzt = λtµzt−1 + λtεt

q = 0.5

Regime 1

Fiscal Limit: Regime 2 PM/AF/AT

1

MP: Rt = R∗

FP: τt = τmax

Transfers: zt = µzt−1 + εt 1− q = 0.5

Regime 2

Regime 1

Fiscal Limit: Switch Between Regimes

1

MP: Rt =

{R∗ + α(πt − π∗), α > 1/βR∗

FP: τt = τmax

Transfers: zt =

{λtµzt−1 + λtεtµzt−1 + εt

Regime 2

1− p11

Regime 1

1− p22

Counterfactual Experiments

I Layers of uncertainty call for a probabilisticdescription of outcomes

I Report equilibrium transition paths conditional onparticular realizations of policies

I decision rules based on true probability distributions

I agents always place probability on alternative futureregimes

I these are counterfactual exercises that induce policyregime surprises every period

Pre-Limit as Transfers Grow

I Dominate forces are rising debt and taxes

I Rising tax rates discourage labor effort and reduceconsumption

I Inflection point in dynamics arises at limit, τmax

I Capital falls when τt < τmax, then rises when τt > τmax,in expectation of a future reduction in tax rates

Pre-Limit as Transfers Grow

2010 2020 2030 2040 2050 2060−4

−2

0

Output (% deviation from 2009)

2010 2020 2030 2040 2050 2060−10

−5

0

Consumption (% deviation from 2009)

2010 2020 2030 2040 2050 2060−5

0

5

10Capital Stock (% deviation from 2009)

2010 2020 2030 2040 2050 2060−8−6−4−2

0

Labor (% deviation from 2009)

2010 2020 2030 2040 2050 20600.2

0.22

0.24

0.26

0.28Tax Rate

2010 2020 2030 2040 2050 20600.5

1

1.5Debt / Output

2010 2020 2030 2040 2050 20601

2

3Inflation (%)

2010 2020 2030 2040 2050 20603

4

5

6Nominal Interest Rate (%)

τmax

Conditional on not triggering fiscal limit

Post-Limit Reneging (λt < 1)

I Monetary policy is active, but can’t stabilize inflation

I Agents believe can return to regime without reneging,but with passive monetary policy

2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 20600

0.5

1

1.5

2Inflation and Expectations (deviation from 2009 rate)

2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 20602

2.2

2.4

2.6

2.8

Ex−ante Real Rate (Rt − E

tπ

t+1)

Expectations

Inflation

Post-Limit Reneging (λt < 1)

I Low real rates reduce savings

I Capital stock declines

2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 2060−10

−5

0Capital Stock (% deviation from 2009 level)

2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 20602

2.2

2.4

2.6

2.8


t−π

t+1)

Post-Limit Passive Monetary Policy

I Monetary policy is passive and λt = 1

I Agents still believe can move to reneging regime

2040 2042 2044 2046 2048 2050 2052 2054 2056 2058 20600

1

2

3


tπ

t+1)

2040 2042 2044 2046 2048 2050 2052 2054 2056 2058 20600

10

20

30Inflation

Post-Limit Passive Monetary Policy

I Possibility of reneging in future increases savings andpostpones consumption

I Drives capital accumulation

2040 2042 2044 2046 2048 2050 2052 2054 2056 2058 2060−10

0

10

20Capital Stock (% deviation from 2009 level)

2040 2042 2044 2046 2048 2050 2052 2054 2056 2058 20600

1

2

3


tπ

t+1)

Conclusions

I Profound uncertainty surrounds the future financingof promised transfers

I Fiscal pressures will likely impair efforts to achieveany inflation objective

I Expected inflation will rise faster than inflation ifhouseholds believe the economy may hit the fiscallimit

I In the presence of a fiscal limit, effects of the limit kickin even during “normal” times

I Underscores that to understand an intrinsically “fiscalissue,” must integrate monetary policy

Documents

“Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020